Reasoning: Syllogism Questions Set 15

Direction (1-5): Each option contains some statements. Determine from which statements the given two conclusions follow.

1. Conclusions:
   I. No orange is grape.
   II. All grapes are apples is a possibility.
   Statements:
   A) Some apples are oranges. No lemon is orange. All lemons are grapes.
   B) Some apples are oranges. No lemon is orange. All grapes are lemons.
   C) All apples are oranges. No lemon is orange. All grapes are lemons.
   D) Some apples are oranges. Some lemons are oranges. No grape is lemon.
   E) None is correct
   
   View Answer

     Option B
   Solution:
   From B) All grapes are lemons.+ No lemon is orange=> All No=No=> No grape is orange or No orange is grape
   All grapes are lemons.+ No lemon is orange+ Some orange is apple =>{All+No} +Some=> No+ Some= Some not reversed=Some apple are not grapes=> All grapes being apple is a possibility is true
     
2. Conclusions:
   I. Some scales are not pencils.
   II. All pens are scales is a possibility.
   Statements:
   A) All pens are pencils. No pencil is eraser. All scales are erasers.
   B) Some pens are pencils. No pen is eraser. All erasers are scales.
   C) All pens are pencils. No pencil is eraser. Some erasers are scales.
   D) Some pens are pencils. Some pencils are erasers. No eraser is scale.
   E) None is correct
   
   View Answer

     Option C
   Solution:
   From C) No pencil is eraser. Some erasers are scales.=> No+ Some = some not reversed= Some scale are not pencil
   All pens are pencils. No pencil is eraser. Some erasers are scales.= =>{All+No} +Some=> No+ Some= Some not reversed=> Some scale are not pen=> All pen being scale is a possibility is true  
3. Conclusions:
   I. Some rupee are dollar.
   II. All pound are dollar is a possibility.
   Statements:
   A) Some dollar are yen. All yen are rupee. No pound is rupee.
   B) All dollar are yen. Some yen are rupee. No pound is rupee.
   C) Some dollar are yen. No yen is rupee. Some pound are yen.
   D) All dollar are yen. Some dollar are rupee. No pound is yen.
   E) None is correct
   
   View Answer

     Option A
   Solution:
   From A) Some dollar are yen. All yen are rupee. => Some+ All= Some => Some Rupees are dollar
   Some dollar are yen. All yen are rupee +No rupee is pound={Some + All} + No=Some + No = Some Not= Some dollar are not Pound. Hence all pound being dollar is a possibility is true
4. Conclusions:
   I. Some site are forum is a possibility.
   II. No forum is blog.
   Statements:
   A) Some blogs are press. All sites are press. No forum is press.
   B) All blogs are press. Some sites are blogs. No forum is press.
   C) All blogs are press. Some sites are press. Some forum are sites.
   D) Some blogs are press. No site is blog. Some forums are sites.
   E) None is correct
   
   View Answer

     Option B
   Solution:
   In B) Some site are blogs + All blogs are press + No press is forum = {Some+ All} + No = Some + No = Some not=> Some site are not forum=> But then Some site are forum is a possibility will be true
   All blogs are press + No press is forum=All+ No= No=> No blog is forum= No forum is blog
   
5. Conclusions:
   I. All pages are comments is a possibility.
   II. Some posts are not pages.
   Statements:
   A) Some pages are sites. Some posts are comments. No comment is site.
   B) No page is site. Some posts are comments. Some comments are sites.
   C) No page is site. Some posts are sites. Some comments are sites.
   D) No page is site. Some posts are sites. Some comments are sites.
   E) None is correct
   
   View Answer

     Option C
   Solution:
   In C) Some comments are sites+ No site is page=> Some+ No= Some not=? Some comments are not page. => All pages being comment is apossibility is true.
   Some posts are sites+ No site is page= Some Not=? Some posts are not page.

Directions (6-8): In each of the questions below, statements are given followed by three conclusions numbered I, II and III. Read all the conclusions and then decide which of the given conclusions do not follow from the given statements.

6. Statements: All red are green. No green is a blue. All white are blue. All blue are black.
   Conclusions:
   I. Some black are green.
   II. Some white are red is a possibility.
   III. Some green are not black.
   A) Only I and III
   B) Only II and III
   C) All I, II and III
   D) Only II
   E) Only III
   
   View Answer

    Option C
   Solution:
   For I. conclusion between black and green. No green is a blue + All blue are black.
   => No + All= Some not reversed=> Some black are not green. I is false
   For II. All red are green. No green is a blue => All+ No=No=> No red is blue Add it to All white are blue.  + No blue is red=> No white is red=> hence II. is false
   For III. Relation between green and black. Done in I.
7. Statements: Some rupee are dollar. All dollar are yen. No yen is a pound. All peso are pound.
   Conclusions:
   I. All rupee are peso is a possibility.
   II. No peso is dollar.
   III. No yen is rupee
   A) Only II and III
   B) Only I and III
   C) Only II
   D) Only III
   E) All follow
   
   View Answer

    Option B
   Solution:
   For I. Relation between  rupee and peso. Solve first three statement first: Some rupee are dollar. All dollar are yen. No yen is a pound=> Some + No= Some rupee are not pound  + All peso are pound. This is the second exceptional case of syllogism as discussed in our notes section. . All peso are pound. + Some rupee are not pound   gives us Some rupee are not peso. Hence I is false
   For II. Relation between Peso and dollar. : All dollar are yen. No yen is a pound=> No dollar is pound; All peso are pound. + No pound is dollar= All+ No= No=> No peso is dollar is true
   For III. Relation between yen and rupee. Some+All=Some => Some Yen is rupee. So III is false
8. Statements: Some lions are dogs. All dogs are cats. Some cats are jungles. All jungles are monkey.
   Conclusions:
   I. Some dogs are monkey
   II. Some jungles are not lions
   III. All jungles being dogs is a possibility.
   A) Only III
   B) Only II and III
   C) All follow
   D) Only I and II
   E) Only I and III
   
   View Answer

    Option D
   Solution:
   I. relation between dogs and  monkey: All dogs are cats. Some cats are jungles. All jungles are monkey. => All + Some + All = No conclusion. Hence I is false
   II. Some lions are dogs. All dogs are cats. Some cats are jungles => Some+All+Some= No conclusion. Hence II is false
   III. Relation between jungles and dogs => All dogs are cats. Some cats are jungles= All+Some= No conclusion= Any possibility between jungles and dogs is true. Hence III follows
   

Direction (9-10): In which of the following options 4^th statement follows from the 1^st three statement?

9. A) Some squares are rectangles. All squares are spheres. No sphere is a cone. All cones being square is a possibility.
   B) All cones are cylinders. Some cones are squares. No square is a rectangle. Some cones being rectangle is a possibility.
   C) Some squares are rectangles. All squares are spheres. No sphere is a cone. All spheres are squares.
   D) All rectangles are squares. All squares are triangles. No triangle is a cone. Some rectangles being cone is a possibility.
   E) Does not follow in any option.
   
   View Answer

     Option B
   Solution:
   In A) Fourth statement is: All cones being square is a possibility.
   => from All squares are spheres. No sphere is a cone.=All+No= No=>No cone is square. Hence False
   In B) Fourth statement is: Some cones being rectangle is a possibility.
   Some cones are squares. No square is a rectangle=>Some+No=Some not=>Some cones are not rectangle. Hence some cones being rectangle is a possibility is true. Hence True
   In C) Fourth statement is: All spheres are squares.
   Some squares are rectangles. All squares are spheres.=> Some+All= Some squares are sphere or some sphere are square. Hence False
   In D) Fourth statement is: Some rectangles being cone is a possibility.
   All rectangles are squares. All squares are triangles. No triangle is a cone =>All+All+No=No =>No rectangle is cone. Hence False
10. A) All rectangles are cones. Some cones are squares. No square is triangle. Some triangles are rectangle.
    B) Some cones are rectangles. Some rectangles are spheres. All spheres are squares. All spheres are Cones.
    C) Some cones are rectangles. Some rectangles are spheres. All spheres are squares. All squares are cone.
    D) All rectangles are cones. Some cones are squares. No square is triangle. Some squares being rectangle is a possibility.
    E) Does not follow in any option.
    
    View Answer

    Option D
    Solution:
    In A) Fourth statement is: Some triangles are rectangle.
    From All rectangles are cones. Some cones are squares. No square is triangle=> All+Some+No= No conclusion. Hence False
    In B) Fourth statement is: All spheres are Cones.
    Some cones are rectangles. Some rectangles are spheres.=> Some+Some No conclusion , Hence False
    In C) Fourth statement is: All squares being Cone is a possibility.
    Some cones are rectangles. Some rectangles are spheres. All spheres are squares.=> Some +Some+All= No conclusion. Hence False
    In D) Fourth statement is: Some squares being rectangle is a possibility.
    All rectangles are cones. Some cones are squares=> All+ Some = No conclusion=> Any possibility is true. Hence True